ISBN: 1-57146-111-6
Binding: Hardcover
Page Number: 238
Year Published: 2003
Based on lectures held at the Center for
Theoretical Sciences in
Taiwan in honor of Louis Nirenbergfs 75th
birthday, the volume
contains both research papers dealing with
various problems in
Partial Differential Equations such as wave
maps, the Navier-Stokes
equations, and Lagrangian submanifolds.
Professor Nirenberg is particularly appreciated
for his generous
encouragement of the development of mathematics
in the Asia-Pacific
region and the mixture of articles by distinguished
mathematicians from Asia and other parts
of the world.
Table of Contents
1 Recent Progress in Conformal Geometry (with
an Emphasis on the
Use of Configuration Spaces) ? ABBAS BAHRI
2 Homotopy Classes in Sobolev Spaces ? HAIM
BREZIS
3 Entire Solutions of a Fully Nonlinear Equation
? SUN-YUNG A.
CHANG, MATTHEW J GURSKY & PAUL C YANG
4 Extremal Functions for a Mean Field Equation
in Two Dimension ?
SUN-YUNG A CHANG, CHIUN-CHUAN CHEN, &
CHANG-SHOU LIN
5 Shocks and very Strong Vertical Diffusion
? YOUSHIKAZU GIGA
6 The Wave Map Problem ? MANOUSSOS G GRILLAKIS
7 Some Regularity Criteria on Suitable Weak
Solutions of the 3-D
Incompressible Axisymmetric Navier-Stokes
Equations - QUANSEN JIU
& ZHOUPING XIN
8 Multiplier Ideals and Microlocalization
? JOSEPH J. KOHN
9 Some Recent Work on Elliptic Systems from
Composite Material ?
YAN YAN LI
10 Bubbling and Quantization in High Dimensions
? FANG HUA LIN
11 Entropy Pairs for Conservation Laws and
H-theorem for the
Boltzmann Equation - TAI-PING LIU, TONG YANG,
& SHIH-HSIEN YU
12 Qualitative Results on the Generalized
Critical KdV Equation ?
YVAN MARTEL & FRANK MERLE
13 The Volume Functional for Lagrangian Submanifolds
- RICHARD
SCHOEN & JON WOLFSON
14 An Algebraic Characterization of the Modified
Korteweg - De
Vries Hierachy ? FRANCOIS TREVES
15 Particle Systems and Partial Differential
Equations ? S.R.S.
VARADHAN
16 An Estimate of the Gap of the first two
Eigenvalues in the
Schrodinger Operator ? SHING-TUNG YAU
ISBN: 1-57146-125-6 / ISBN: 7-03-010271-1
Binding: Hardcover
Page Number: 247
Year Published: 2002
Since the publication of the seminal work
of H. Federer which
gives a rather complete and comprehensive
discussion on the
subject, the geometric measure theory has
developed in the last
three decades into an even more cohesive
body of basic knowledge
with an ample structure of its own, established
strong ties with
many other subject areas of mathematics and
made numerous new
striking applications. The present book is
intended for the
researchers in other fields of mathematics
as well as graduate
students for a quick overview on the subject
of the geometric
measure theory with emphases on various basic
ideas, techniques
and their applications in problems arising
in the calculus of
variations, geometrical analysis and nonlinear
partial
differential equations.
This graduate-level treatment of Geometric
Measure Theory
illustrates with concrete examples and emphasizes
basic ideas and
techniques with their applications to the
calculus of variations,
geometrical analysis, and non-linear PDEs.
The book, in addition
to a full index and bibliography, include
eight main chapters:
1 Hausdoff Measure
1.1 Preliminaries, Definitions and Properties
1.2 Isodiametric Inequality and Hn = Ln
1.3 Densities
1.4 Some Further Extensions Related to Hausdorff
Measures
2 Fine Properties of Functions and Sets and
Their Applications
2.1 Lebesgbue Points of Sobolev Functions
2.2 Self-Similar Sets
2.3 Federerfs Reduction Principle
3 Lipschitz Functions and Rectifiable Sets
3.1 Lipschitz Functions
3.2 Submanifolds of R n+k
3.3 Countably n-Rectifiable Sets
3.4 Weak Tangent Space Property, Measures
in Cones and
Rectifiability
3.5 Density and Rectifiability
3.6 Orthogonal Projections and Recifiability
4 The Area and Co-area Formulae
4.1 Area Formula and Its Proof
4.2 Co-area Formula
4.3 Some Extensions and Remarks
4.4 The First and Second Variation Formula
5 BV Functions and Sets of Finite Perimeter
5.1 Introduction and Definitions
5.2 Properties
5.3 Sobolev and Isoperimetric Inequalities
5.4 The Co-area Formula for BV Functions
5.5 The Reduced Boundary
5.6 Further Properties and Results Relative
to BV Functions
6 Theory of Varifolds
6.1 Measures of Oscillation
6.2 Basic Definitions and the First Variation
6.3 Monotonicity Formula and Isoperimetric
Inequality
6.4 Rectifiability Theorem and Tangent Cones
6.5 The Regularity Theory
7 Theory of Currents
7.1 Forms and Currents
7.2 Mapping Currents
7.3 Integral Rectifiable Currents
7.4 Deformation Theorem
7.5 Rectifiability of Currents
7.6 Compactness Theorem
8 Mass Minimizing Currents
8.1 Properties of Area Minimizing Currents
8.2 Excess and Height Bound
8.3 Excess Decay Lemmas and Regularity Theory
ISBN: 0-471-46617-4
Hardcover
256 pages
September 2003
Author Information
An indispensable guide to understanding wavelets
Elements of Wavelets for Engineers and Scientists
is a guide to
wavelets for "the rest of us"?practicing
engineers and
scientists, nonmathematicians who want to
understand and apply
such tools as fast Fourier and wavelet transforms.
It is
carefully designed to help professionals
in nonmathematical
fields comprehend this very mathematically
sophisticated topic
and be prepared for further study on a more
mathematically
rigorous level.
Detailed discussions, worked-out examples,
drawings, and drill
problems provide step-by-step guidance on
fundamental concepts
such as vector spaces, metric, norm, inner
product, basis,
dimension, biorthogonality, and matrices.
Chapters explore . . .
Functions and transforms
The sampling theorem
Multirate processing
The fast Fourier transform
The wavelet transform
QMF filters
Practical wavelets and filters
. . . as well as many new wavelet applications-image
compression,
turbulence, and pattern recognition, for
instance-that have
resulted from recent synergies in fields
such as quantum physics
and seismic geology.
Elements of Wavelets for Engineers and Scientists
is a must for
every practicing engineer, scientist, computer
programmer, and
student needing a practical, top-to-bottom
grasp of wavelets.
October 2003, ISBN 1-4020-1487-2, Paperback
October 2003, ISBN 1-4020-1486-4, Hardbound
Book Series: NATO SCIENCE SERIES: II: Mathematics,
Physics and
Chemistry : Volume 115
Commutative Algebra, Singularities and Computer
Algebra presents
current trends in commutative algebra, algebraic
combinatorics,
singularity theory and computer algebra,
and highlights the
interaction between these disciplines. Contributions
by leading
international mathematicians thoroughly discuss
topics in:
modules theory, integrally closed ideals
and determinantal
ideals, singularities in projective spaces
and Castelnuovo-Mumford
regularity, Groebner and SAGBI basis, and
the use of the computer
packages Bergman, CoCoA and SINGULAR.
Contents and Contributors
Association for Flag Configuration; C. Borcea.
Grobner bases and
determinantal ideals; W. Bruns, A. Conca.
Bounds for Castelnuovo-Mumford
regularity in terms of degrees of defining
equations; M. Chardin.
The Computer Algebra Package Bergman: Current
State; J. Backelin,
S. Cojocaru, V. Ufnarovski. Monomialization
and ramification of
valuations; S.D. Cutkosky. Hyperplane arrangements,
M-tame
polynomials and twisted cohomology; A. Dimca.
A note on the
Intersection of Veronese Surfaces; D. Eisenbud,
K. Hulek, S.
Popescu. Rank one Maximal Cohen-Macaulay
modules over
singularities of type Y3 1+ Y32 + Y33 + Y34;
V. Ene, D. Popescu.
Towards a theory of Gorenstein m-primary
integrally closed
ideals; S. Goto, F. Hayasaka, S. Kasuga.
Universal Grobner bases,
integer programming and finite graphs; H.
Ohsugi, T. Kitamura, T.
Hibil. Torsion in tensor powers and flatness;
C. Ionescu. Basic
Tools for Computing in Multigraded Rings;
M. Kreuzer, L. Robbiano.
A Problem in Group Theory solved by Computer
Algebra; G. Pfister.
On curves of small degree on a normal rational
surface Scroll; P.
Schenzel. On SAGBI Bases and Resultants;
A. Torstensson, V.
Ufnarovski, H. Ofverbeck. Modules of G-dimension
zero over local
rings with the cube of maximal ideal being
zero; Y. Yoshino.
October 2003, ISBN 1-4020-1574-7, Hardbound
Book Series: FUNDAMENTAL THEORIES OF PHYSICS
: Volume 132
This book is the first to present an overview
of higher-order
Hamilton geometry with applications to higher-order
Hamiltonian
mechanics. It is a direct continuation of
the book The Geometry
of Hamilton and Lagrange Spaces, (Kluwer
Academic Publishers,
2001). It contains the general theory of
higher order Hamilton
spaces H(k)n, k?1, semisprays, the canonical
nonlinear
connection, the N-linear metrical connection
and their structure
equations, and the Riemannian almost contact
metrical model of
these spaces. In addition, the volume also
describes new
developments such as variational principles
for higher order
Hamiltonians; Hamilton-Jacobi equations;
higher order energies
and law of conservation; Noether symmetries;
Hamilton subspaces
of order k and their fundamental equations.
The duality, via
Legendre transformation, between Hamilton
spaces of order k and
Lagrange spaces of the same order is pointed
out. Also, the
geometry of Cartan spaces of order k =1 is
investigated in detail.
This theory is useful in the construction
of geometrical models
in theoretical physics, mechanics, dynamical
systems, optimal
control, biology, economy etc.
Audience: Mathematicians, geometers, physicists
and engineers.
The volume can be recommended as a supplementary
graduate text.